Semiconductor devices such as logic and memory devices are typically fabricated by a sequence of processing steps applied to a substrate or wafer. The various features and multiple structural levels of the semiconductor devices are formed by these processing steps. For example, lithography among others is one semiconductor fabrication process that involves generating a pattern on a semiconductor wafer. Additional examples of semiconductor fabrication processes include, but are not limited to, chemical-mechanical polishing, etch, deposition, and ion implantation. Multiple semiconductor devices may be fabricated on a single semiconductor wafer and then separated into individual semiconductor devices.
Inspection processes are used at various steps during a semiconductor manufacturing process to detect defects on wafers to promote higher yield. As design rules and process windows continue to shrink in size, inspection systems are required to capture a wider range of physical defects on wafer surfaces while maintaining high throughput.
Semiconductor devices are increasingly valued based on their energy efficiency, rather than speed alone. For example, energy efficient consumer products are more valuable because they operate at lower temperatures and for longer periods of time on a fixed battery power supply. In another example, energy efficient data servers are in demand to reduce their operating costs. As a result, there is a strong interest to reduce the energy consumption of semiconductor devices.
Leakage current through insulator layers is a major energy loss mechanism of semiconductor devices manufactured at the 65 nm technology node and below. In response, electronic designers and manufacturers are adopting new materials (e.g., hafnium silicate (HfSiO4), nitrided hafnium silicates (HfSiON), hafnium dioxide (HfO2), zirconium silicate (ZrSiO4), etc.) with higher dielectric constants than traditional materials (e.g., silicon dioxide). These “high-k” materials reduce leakage current and enable the manufacture of smaller sized transistors.
Along with the adoption of new dielectric materials, the need has arisen for measurement tools to characterize the dielectric properties and band structures of high-k materials early in the manufacturing process. More specifically, high throughput monitoring tools are required to monitor and control the deposition of high-k materials during wafer manufacture to ensure a high yield of finished wafers. Early detection of deposition problems is important because the deposition of high-k materials is an early process step of a lengthy and expensive manufacturing process. In some examples, a high-k material is deposited on a wafer at the beginning of a manufacturing process that takes over one month to complete.
The performance of a logic gate is commonly characterized in terms of electrical characteristics such as equivalent oxide thickness (EOT), leakage current, threshold voltage, leakage EOT, and breakdown voltage. During device processing it is important to monitor and control these parameters. These electrical characteristics may be studied by a variety of methods including electrical measurements, transmission electron microscopy, x-ray spectroscopy and scattering, atomic force microscopy, and photoelectronic spectroscopy. Currently, however, these measurement technologies suffer from any of a number of limitations. In some cases, the measurements require destruction of the sample. In some cases, many post-deposition processing steps must be completed before measurements can occur. In some cases, the measurement technology is slow, and must be separated from the production line.
Optical metrology tools offer the possibility of high throughput, in-line, non-destructive characterization of electrical characteristics of gate structures. In particular, the spectroscopic ellisometry (SE) measurement technique includes a parametric representation of a measured optical dispersion. In some examples, the parameterized model is representative of a dielectric function that has a direct relation to the band gap parameter; a key indicator of the electrical performance of the gate structure. In general, the particular parameterization is selected to reduce the number of unknown parameters and decrease correlations among parameters.
In some examples, the optical response of one or more high-K dielectric layers is predicted based on a direct inversion method. These methods are described by way of example in J. Price et al., “Identification of interfacial defects in high-k gate stack films by spectroscopic ellipsometry,” J. Vac. Sci. Technol. B 27 (1), 310 (2009) and J. Price et al., “Identification of sub-band-gap absorption features at the HfO2/Si(100) interface via spectroscopic ellipsometry,” APL 91, 061925 (2007), the subject matter of each is incorporated herein in its entirety. However, direct inversion methods are computationally burdensome, very sensitive to statistical measurement errors, and do not provide a physically based model of the measured structure (i.e., the optical functions do not satisfy the Kramers-Kronig consistency condition). As a result, the utility of direct inversion methods for high-throughput inspection and process control is limited. In addition, the direct inversion method involves an ill-defined mathematical problem. SE measurements provide two values (e.g., α and β, Ψ and Δ, etc.) for each measured wavelength, but the model inversion must generate estimates for three unknowns. For example, the inversion might provide estimates for the real (ε1) and imaginary (ε2) parts of the dielectric function and film thickness. In another example, the inversion might provide estimates for the refractive index (n) and extinction coefficient (k) and film thickness. The solution to this ill-defined problem requires the introduction of artificial, simplifying assumptions that introduce undesireable errors.
In some other examples, the optical response of one or more high-K dielectric layers is predicted based on a Bruggeman Effective Model Approximation (BEMA) model. The BEMA model represents the dielectric function of the layer as an effective composition of assumed dielectric functions of constituents. The optimized effective composition is then related to the composition of the dielectric layer of interest. In general, the BEMA model is based on Kramers-Kronig consistent dielectric functions of constituents, and thus is itself Kramers-Kronig consistent. As a result, the BEMA model yields physically reasonable results. However, the value of the band gap as derived from the BEMA model is an indirect measurement that requires a reference to provide meaningfully accurate results.
Both the BEMA and the direct inversion method are used to extract dispersion curves (e.g., the real (ε1) and the imaginary (ε2) parts of the dielectric function, or refractive index (n) and extinction coefficient (k)) from SE measurements. Subsequently, the calculated dispersion curves must be interpolated in the energy range of interest to evaluate the band gap. The accuracy of the band gap estimate depends strongly on the choice of the energy of interest for band gap interpolation. Moreover, since band gap must be indirectly derived from the calculated dispersion curves, a reference is required to provide accurate results. For these practical reasons, both BEMA and direct inversion are limited in their ability to accurately monitor band gap.
In some other examples, a Tauc-Lorentz model or a Cody-Lorentz model is employed as described by way of example in A. S. Ferlauto et al., “Analytical model for the optical functions of amorphous semiconductors from the near-infrared to ultraviolet: Application in thin film photovoltaics,” J. Appl. Phys. 92, 2424 (2002), the subject matter of which is incorporated herein in its entirety. In these models, the imaginary part of the dielectric function is represented by a parameterized dispersion function, and the real part of the dielectric function is determined based on enforcement of Kramers-Kronig consistency. Model parameters (e.g., optical function parameters and thicknesses) are evaluated by fitting modeled spectra to measured spectra by numerical regression. The validity and limitations of the models are assessed by statistical evaluation of fitting quality and confidence limits of model parameters.
An important limitation of the conventional Cody-Lorentz function is that it has discontinuous derivatives over the energy range, E, and the resonant energy range, E0, at the Urbach transition energy level, ET. This leaves the dispersion model mathematically ill-defined, leaving open the possibility that the model will yield results that have no relation to real, physical features of the material. Moreover, continuity of derivatives is an important characteristic of any optical model subject to optimization in SE metrology. In particular, a discontinuity of derivatives may make the optimization process computationally unstable.
Accordingly, it would be advantageous to develop high throughput methods and/or systems for characterizing high-k dielectric layers early in the manufacturing process. In particular, it would be advantageous to develop a robust, reliable, and stable approach to in-line SE metrology of gate stacks including high-K dielectrics.